Abstract
We consider the optical fiber channel modelled by the nonlinear Schrödinger equation with additive white Gaussian noise and with large signal-to-noise ratio. For the small dispersion case we present the approach to analyze the stochastic nonlinear Schrödinger equation. Taking into account the averaging procedure (frequency filtering) of the output signal detector we find the first corrections in small dispersion parameter to the correlators of the input signal recovered by the backward propagation. These correlators are the important ingredients for the calculation of the channel capacity and the optimal input signal distribution. We assert that the information channel characteristics essentially depend on the procedures of the output signal filtering and the recovery of the transmitted signal.
Highlights
The problem of analytical calculations of characteristics for a given information channel is of great importance in the information theory due to the practically significant applications of optical fibers
In our work we consider the problem of the signal propagation in a noisy information channel where the propagation is governed by the stochastic nonlinear Schrodinger equation (NLSE) with the additive white Gaussian noise for the case of small dispersion and the large signal-to-noise power ratio (SNR)
We demonstrate how the channel informational characteristics depend on the procedure of the output signal detecting and the algorithm of the input signal recovery on the base of the filtered output signal, see Sec. 4
Summary
The problem of analytical calculations of characteristics for a given information channel is of great importance in the information theory due to the practically significant applications of optical fibers. We present the correlators of the input signal X(t) recovered from the noisy channel and the conditional probability density function up to the first corrections in dispersion parameter, see Sec. 5. In our calculatio√ns we ρ(t) = |X(t)| ≈ Pave present the input signal in the rk gk (t), and the constant form X(t) = ρ(t) exp{iφ0(t)}, where over the subintervals T0 phase φ0(t) is smoothed function in such a way that all time derivates (φ0, φ0) are localized on the borders of subintervals T0, and if one neglects the overlapping φ0(t)gk(t), φ0(t)gk(t) may be considered as zero.
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